“The Senate’s duty is to advise and consent,” said Sen. Ted Cruz, Texas Republican and presidential candidate. “You know what? The Senate is advising right now. We’re advising that a lame-duck president in an election year is not going to ... more >

Congressional bigwigs and the presidential field brushed aside their condolences Sunday and girded for an election-year fight over how and when to replace Supreme Court Justice Antonin Scalia, the colorful conservative justice who died over the weekend.

The fast-moving dispute pitted Democrats, who said the Constitution compels President Obama to act, against Republicans, who said the founding document will become irrelevant if the court tilts to the left.

Senate Democrats said Sunday that they can’t find the constitutional clause that says Mr. Obama has to sit back and let his successor fill the vacancy, while Republicans said the high court can function with eight members for now, giving voters the chance to shape its future.

News of Justice Scalia’s death in Texas, apparently of natural causes, was only a few hours old Saturday before Senate Democrats urged Mr. Obama to send them a nominee and the Republican majority vowed to ignore it.

“The Senate’s duty is to advise and consent,” said Sen. Ted Cruz, Texas Republican and presidential candidate. “You know what? The Senate is advising right now. We’re advising that a lame-duck president in an election year is not going to be able to tip the balance of the Supreme Court — that we’re going to have an election.”

Justice Scalia, who was 79, was found dead in his room at a West Texas resort early Saturday after he didn’t come out for breakfast.

Outspoken and often humorous, he endeared himself to conservatives during his three decades on the bench while vexing liberals who frequently disagreed with him yet admired his candor.

Mr. Obama said he will nominate a replacement in “due time,” but Senate Majority Leader Mitch McConnell, Kentucky Republican, swiftly ruled out a vote this year.

“The American people should have a voice in the selection of their next Supreme Court justice,” Mr. McConnell said. “Therefore, this vacancy should not be filled until we have a new president.”

Other Republicans said it has been a “standard practice” for 80 years not to nominate and confirm Supreme Court justices in a presidential election year.

Justice Anthony M. Kennedy was confirmed to his seat in 1988 — the final year of Ronald Reagan’s presidency — though Republicans contended that Senate Democrats stretched out that fight by vehemently opposing and rejecting a prior pick, Robert Bork.

Democrats rejected the Republicans’ posture Sunday, saying they have an obligation to follow the Founding Fathers’ constitutional design and fill the court, which is poised to rule this term on Mr. Obama’s amnesty program for certain illegal immigrants, how Obamacare’s birth control rules should apply to religious nonprofits and whether public-sector unions can collect fees from workers who do not join.

“I can’t find a clause that says ‘except when there’s a year left in the term of a Democratic president,’” said Sen. Elizabeth Warren, Massachusetts Democrat.

Sen. Bernard Sanders, a Vermont independent who is challenging former Secretary of State Hillary Clinton for the Democratic presidential nomination, echoed Ms. Warren, saying the Constitution is “pretty clear” about what should happen when there is a vacancy.

The standoff adds a remarkable wrinkle to an already challenging year on Capitol Hill. Republicans in charge of both chambers say there are few opportunities for bipartisan agreement, though mental health care reform could be one.

Instead, House Speaker Paul D. Ryan, Wisconsin Republican, wants to put forth an agenda of “ideas,” offering voters a clear contrast to Mr. Obama’s agenda. Mr. McConnell wants to get back to basics by passing a budget and all dozen appropriation bills in a legislative year shortened by this summer’s nominating conventions and November’s general elections.

The debate already is spilling onto the campaign trail in South Carolina, where Mr. Cruz said his chief rival, businessman Donald Trump, could not be trusted to nominate a worthy replacement.

“It is abundantly clear that Donald Trump is not a conservative, he will not invest the capital to confirm a conservative,” Mr. Cruz told ABC’s “This Week.”

Mr. Cruz said Americans’ right to bear arms and other “basic liberties” would be at risk if Mr. Obama is able to tilt the court toward a liberal majority.

“We’re one justice away from the Second Amendment begin written out,” he said.

The other sitting senator in the race, Sen. Marco Rubio of Florida, said Mr. Obama is free to make a nomination but Republicans will push aside confirmation.

“There comes a point in the last year of the president, especially in their second term, where you stop nominating or you stop the advise-and-consent process,” Mr. Rubio told “Fox News Sunday.”

Former Florida Gov. Jeb Bush, who is hoping to give his Republican presidential bid a boost in South Carolina, said he thinks Mr. Obama will pick someone who is “out of the mainstream,” though it is up to Mr. McConnell to decide whether to hold a vote on a nominee.